MATLAB histogram2 in MATLAB^®

Learn how to make 9 histogram2 charts in MATLAB, then publish them to the Web with Plotly.

Histogram of Vectors

Generate 10,000 pairs of random numbers and create a bivariate histogram. The histogram2 function automatically chooses an appropriate number of bins to cover the range of values in x and y and show the shape of the underlying distribution.

x = randn(10000,1); y = randn(10000,1); h = histogram2(x,y)

h = 
  Histogram2 with properties:

             Data: [10000x2 double]
           Values: [25x28 double]
          NumBins: [25 28]
        XBinEdges: [1x26 double]
        YBinEdges: [1x29 double]
         BinWidth: [0.3000 0.3000]
    Normalization: 'count'
        FaceColor: 'auto'
        EdgeColor: [0.1500 0.1500 0.1500]

  Show all properties

xlabel('x')
ylabel('y')

fig2plotly()

When you specify an output argument to the histogram2 function, it returns a histogram2 object. You can use this object to inspect the properties of the histogram, such as the number of bins or the width of the bins.

Find the number of histogram bins in each dimension.

nXnY = h.NumBins

fig2plotly()

nXnY = 1×2

    25    28

## Specify Number of Histogram Bins Plot a bivariate histogram of 1,000 pairs of random numbers sorted into 25 equally spaced bins, using 5 bins in each dimension. x = randn(1000,1); y = randn(1000,1); nbins = 5; h = histogram2(x,y,nbins)

h = 
  Histogram2 with properties:

             Data: [1000x2 double]
           Values: [5x5 double]
          NumBins: [5 5]
        XBinEdges: [-4 -2.4000 -0.8000 0.8000 2.4000 4]
        YBinEdges: [-4 -2.4000 -0.8000 0.8000 2.4000 4]
         BinWidth: [1.6000 1.6000]
    Normalization: 'count'
        FaceColor: 'auto'
        EdgeColor: [0.1500 0.1500 0.1500]

  Show all properties

Find the resulting bin counts.

counts = h.Values

fig2plotly()

counts = 5×5

     0     2     3     1     0
     2    40   124    47     4
     1   119   341   109    10
     1    32   117    33     1
     0     4     8     1     0

## Adjust Number of Histogram Bins Generate 1,000 pairs of random numbers and create a bivariate histogram. x = randn(1000,1); y = randn(1000,1); h = histogram2(x,y)

h = 
  Histogram2 with properties:

             Data: [1000x2 double]
           Values: [15x15 double]
          NumBins: [15 15]
        XBinEdges: [1x16 double]
        YBinEdges: [1x16 double]
         BinWidth: [0.5000 0.5000]
    Normalization: 'count'
        FaceColor: 'auto'
        EdgeColor: [0.1500 0.1500 0.1500]

  Show all properties

Use the `morebins` function to coarsely adjust the number of bins in the x dimension.

nbins = morebins(h,'x');
nbins = morebins(h,'x')

fig2plotly()

nbins = 1×2

    19    15

Use the `fewerbins` function to adjust the number of bins in the y dimension.

nbins = fewerbins(h,'y');
nbins = fewerbins(h,'y')

fig2plotly()

nbins = 1×2

    19    11

Adjust the number of bins at a fine grain level by explicitly setting the number of bins.

h.NumBins = [20 10];

fig2plotly()

Color Histogram Bars by Height

Create a bivariate histogram using 1,000 normally distributed random numbers with 12 bins in each dimension. Specify FaceColor as 'flat' to color the histogram bars by height.

h = histogram2(randn(1000,1),randn(1000,1),[12 12],'FaceColor','flat');
colorbar

fig2plotly()

Tiled Histogram View

Generate random data and plot a bivariate tiled histogram. Display the empty bins by specifying ShowEmptyBins as 'on'.

x = 2randn(1000,1)+2; y = 5randn(1000,1)+3; h = histogram2(x,y,'DisplayStyle','tile','ShowEmptyBins','on');

Specify Bin Edges of Histogram

Generate 1,000 pairs of random numbers and create a bivariate histogram. Specify the bin edges using two vectors, with infinitely wide bins on the boundary of the histogram to capture all outliers that do not satisfy |x|<2.

x = randn(1000,1); y = randn(1000,1); Xedges = [-Inf -2:0.4:2 Inf]; Yedges = [-Inf -2:0.4:2 Inf]; h = histogram2(x,y,Xedges,Yedges)

h = 
  Histogram2 with properties:

             Data: [1000x2 double]
           Values: [12x12 double]
          NumBins: [12 12]
        XBinEdges: [1x13 double]
        YBinEdges: [1x13 double]
         BinWidth: 'nonuniform'
    Normalization: 'count'
        FaceColor: 'auto'
        EdgeColor: [0.1500 0.1500 0.1500]

  Show all properties

When the bin edges are infinite, `histogram2` displays each outlier bin (along the boundary of the histogram) as being double the width of the bin next to it. Specify the `Normalization` property as `'countdensity'` to remove the bins containing the outliers. Now the volume of each bin represents the frequency of observations in that interval.

h.Normalization = 'countdensity';

fig2plotly()

Normalized Histogram

Generate 1,000 pairs of random numbers and create a bivariate histogram using the 'probability' normalization.

x = randn(1000,1); y = randn(1000,1); h = histogram2(x,y,'Normalization','probability')

h = 
  Histogram2 with properties:

             Data: [1000x2 double]
           Values: [15x15 double]
          NumBins: [15 15]
        XBinEdges: [1x16 double]
        YBinEdges: [1x16 double]
         BinWidth: [0.5000 0.5000]
    Normalization: 'probability'
        FaceColor: 'auto'
        EdgeColor: [0.1500 0.1500 0.1500]

  Show all properties

Compute the total sum of the bar heights. With this normalization, the height of each bar is equal to the probability of selecting an observation within that bin interval, and the heights of all of the bars sum to 1.

S = sum(h.Values(:))

fig2plotly()

S = 1

## Adjust Histogram Properties Generate 1,000 pairs of random numbers and create a bivariate histogram. Return the histogram object to adjust the properties of the histogram without recreating the entire plot. x = randn(1000,1); y = randn(1000,1); h = histogram2(x,y)

h = 
  Histogram2 with properties:

             Data: [1000x2 double]
           Values: [15x15 double]
          NumBins: [15 15]
        XBinEdges: [1x16 double]
        YBinEdges: [1x16 double]
         BinWidth: [0.5000 0.5000]
    Normalization: 'count'
        FaceColor: 'auto'
        EdgeColor: [0.1500 0.1500 0.1500]

  Show all properties

Color the histogram bars by height.

h.FaceColor = 'flat';

fig2plotly()

Change the number of bins in each direction.

h.NumBins = [10 25];

fig2plotly()

Display the histogram as a tile plot.

h.DisplayStyle = 'tile';
view(2)

fig2plotly()

Saving and Loading Histogram2 Objects

Use the savefig function to save a histogram2 figure.

histogram2(randn(100,1),randn(100,1));
savefig('histogram2.fig');
close gcf

fig2plotly()

Use openfig to load the histogram figure back into MATLAB. openfig also returns a handle to the figure, h.

h = openfig('histogram2.fig');

Use the findobj function to locate the correct object handle from the figure handle. This allows you to continue manipulating the original histogram object used to generate the figure.

y = findobj(h,'type','histogram2')

y = 
  Histogram2 with properties:

             Data: [100x2 double]
           Values: [7x6 double]
          NumBins: [7 6]
        XBinEdges: [-3 -2 -1 0 1 2 3 4]
        YBinEdges: [-3 -2 -1 0 1 2 3]
         BinWidth: [1 1]
    Normalization: 'count'
        FaceColor: 'auto'
        EdgeColor: [0.1500 0.1500 0.1500]

  Show all properties